Rigidity of lattice actions on boundaries

  • Mitul Islam (MPI MiS, Leipzig)
E2 10 (Leon-Lichtenstein)


A uniform lattice in SL_n(R) with n at least 3 does not admit non-trivial deformations in SL_n(R), thanks to Margulis super-rigidity. However, such a lattice has a natural action on the Furstenberg boundary. Then, a natural question is whether the lattice can be deformed in this (huge) homeomorphism group of the Furstenberg boundary. We prove a semi-conjugacy rigidity result for such deformations. Surprisingly, we also show that no such rigidity holds for the visual boundary of the symmetric space SL_n(R)/SO_n. This is joint work with Chris Connell, Thang Nguyen, and Ralf Spatzier.

Antje Vandenberg

MPI for Mathematics in the Sciences Contact via Mail

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